This is a preliminary study into convergence and termination of a sequential approximate optimization algorithm based on convex diagonal quadratic subproblems in direct topology optimization. The direct problem is characterised by a large numberof nonlinear equality constraints, hence the method forms part of a general large-scale nonlinear programming paradigm. In structural optimization globally convergent algorithms based on separable and conservative approximations are popular due to minimal storage requirements and minimal function evaluations, in addition to the fact that a trust-region need not be reduced to effect global convergence. However, these methods are restricted to inequality constrained problems. It is demonstrated that the convergence and termination properties that follow from the filtered acceptance of iterates in a trust-region framework can be effected in general nonlinear programming by conditionally increasing the curvature (“conservatism”) of the approximate subproblems, without reducing the trust-region, or even, by neglecting the trust-region all-together. A large-scale instance of the direct formulated slope constrained MBB design problem is considered for numerical experimentation.